Eigenvalues of the negative Laplacian for arbitrary multiply connected domains

摘要

The purpose of this paper is to derive some interesting asymptotic formulae forspectra of arbitrary multiply connected bounded domains in two or three dimensions, linked withvariation of positive distinct functions entering the boundary conditions, using the spectral function∑k=1∞{μk(σ1,…,σn)+P}?2asP→∞. Further results may be obtained.